Quantum-defect theory of double-minimum states inH2

Scattering theory is used to calculate the vibronic energy levels of the interacting double-minimum states in ${\mathrm{H}}_2$. The calculation is based on the accurate ab initio fixed-nuclei energies of Wolniewicz and Dressler. From these a nondiagonal reaction matrix is extracted whose elements are nuclear-coordinate dependent and involve singly and doubly excited channels. The treatment bypasses the state-by-state evaluation of vibronic coupling, and yields in principle the entire vibronic Rydberg spectrum associated with the ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$ 1${\mathrm{\sigma }}_{\mathrm{g}}$ and 1${\mathrm{\sigma }}_{\mathrm{u}}$ cores. The first forty experimental levels are reproduced quite accurately.